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Hanming Liu, Department of Pure Mathematics, University of Waterloo

"Proof of Smale's Theorem"

I will present the proof of Smale's theorem about the existence of gradient-like vector fields satisfying the Smale condition.

M3 4206

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"Spectral curves and the Hitchin system"

I will give an overview of how spectral curves are constructed in the context of Higgs bundles, and discuss how they are used in the study of the Hitchin system.

MC 5479

Zoom link: https://uwaterloo.zoom.us/j/94942581597?pwd=cWhzelpQWXBVakkrZUVWVkFhMmV1dz09

Talk #1: (1:00pm-2:00pm)

Amanda Petcu

"The $G_2$ Laplacian flow and Laplacian solitons"

Erik Seguin, Department of Pure Mathematics, University of Waterloo

"Haagerup's noncommutative Grothendieck inequality (cont.)"

We will continue to prove things related to and on the subject of the NCG theorem. Possibly we will finish the proof of the theorem this week, and possibly not; we conjecture that no third option exists, but we are unable to prove this claim at present. Time permitting, we may attempt to prove this rigorously; this attempt is unlikely to be successful, veracity of the claim notwithstanding.

Talk #1 Valentio Iverson: Powerfree Sieve on Prime Inputs

Abstract: In recent years, there have been several results on the density of integer tuples (a_1,...,a_n) such that f(a_1,...,a_n), for some fixed integer polynomial f, is squarefree. In this talk, we restrict to the case of prime inputs and prove similar results.

Talk #2 Gian Sanjaya: Density of Restricted Polynomials with Squarefree Discriminant

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Vector bundles on toric varieties"

We study vector bundles on toric varieties and a classification theorem due to Klyachko.

This seminar will be held both online and in person:

• Room: MC 5479
• Zoom link: https://uwaterloo.zoom.us/j/98347327227?pwd=anFGNjRsd0ZPUk10SW9vQVNqL3Z0UT09

Cynthia Dai, Department of Pure Mathematics, University of Waterloo

"Properties of Schemes"

We will talk about some properties of schemes, including possibly integral, separated, and proper, if time permits.

MC 5403

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We will be reading Ben Castle’s paper.

MC 5479

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Pseudo-Gradients and the Smale Condition"

 I will continue the discussion of pseudo-gradients that was started last time. I will talk in short detail about how the topology of the level sets change as we cross critical points of a Morse function and on the stable and unstable manifolds. I will discuss in detail the Smale condition and the space of trajectories of pseudo-gradients with a view towards the construction of the Morse complex.

M3 4206

Talk #1: (1:00pm-2:15pm)

Jing Xuan Chen

"Holomorphic bisectional curvature"

The bisectional curvature on a Kähler manifold (M,J) is defined as H(X,Y)=R(X,JX,JY,Y) for unit vectors X,Y. We will see what we can prove about a compact connected Kähler manifold if we assume that it has positive bisectional curvature.

Talk #2: (2:30pm-4:00pm)

Spiro Karigiannis

"The deTurck trick demystified"